本論文著重於波動性預測、風險值的衡量以及SGT分配於風險管理之應用，共包含三個部份。第一部份為「GARCH-SGED模型之中國股市波動性預測」、第二部份為「能源商品的風險－厚尾GARCH模型之應用」與第三部份為「SGT分配在風險值估計所扮演的角色」。將此三部份的內容簡述如下。
第一部份使用GARCH-N與GARCH-SGED模型，探討資產報酬率分配的設定對樣本外波動性預測績效的影響。實證資料採取中國兩大股票市場(上海綜合股價指數與深圳綜合股價指數)，其用意在於進行大陸新興市場之分析，較一般已開發市場更有趣且更具吸引力。實證結果指出，不論是以MSE或MAE作為比較準則，在不同的預測期間，GARCH-SGED模型對大陸股票市場之波動性預測能力皆優於GARCH-N模型。同時，DM檢定統計量進一步證實GARCH-SGED模型顯著優於GARCH-N模型。此結果隱含具偏態及厚尾特性的分配在波動性預測的重要性，尤其是新興國家的金融市場。
第二部分導出Politis(2004)之厚尾分配(HT-distribution)的臨界值公式，藉由此公式將有助於模型樣本外風險值的計算。實證應用則選取GARCH-N、GARCH-t與GARCH-HT等三個不同分配下的GARCH模型，估計一天的絕對風險值，並比較其在風險管理上的績效表現。本文使用三個模型計算五個能源商品現貨(西德州中級原油、布蘭特原油、熱燃油、丙烷與汽油)的多頭部位風險值，並以準確性及效率性兩個層面進行風險值績效分析。實證結果發現，在資產報酬率具有高峰、厚尾特性下，GARCH-HT模型之風險值估計，於所有信心水準下，均最具準確性。此外，MRSB指出，GARCH-HT在較高的信心水準下，所估計出的風險值亦普遍最具效率性。此結果顯示HT分配，特別在能源商品的風險值估計時，是相當合適的。
第三部份則透過風險值的觀點來評估國際原油市場的風險。本部分以適合捕捉波動性叢聚現象的GARCH模型為基礎，並結合兼具厚尾、高峰及偏態特性之SGT分配建構GARCH-SGT模型來估計西德州中級原油現貨報酬之一日風險值。藉由一系列之風險值績效評估準則，實證結果指出在不同的信心水準下，GARCH-SGT模型所估計之風險值，顯著優於傳統研究經常使用之GARCH-T或GARCH-GED模型。因此，SGT分配之假設確實有助於西德州中級原油之風險值預測，意味著風險值模型，同時考量厚尾、高峰及偏態確有其必要性。此一實證結果提供了GARCH-SGT在風險衡量上，為一穩健之風險值估計方法的有利證據。

The purpose of this dissertation is to contribute to the literature on volatility forecasting and its application to risk management (Value-at-Risk) which comprises three parts. The first part of the dissertation is entitled “Predicting the Volatility of Stock Indices in China using GARCH Models with Skewed-GED Distribution”, the second part is named “Modelling Risk for Energy Commodities via Fat-Tailed GARCH Models”, and the last one is “Daily Volatility Forecasts with Application to Risk Management: The Role of SGT Distribution in VaR Estimation”. A brief introduction of these three parts can be summarized as follows: 
The first part investigates how specification of return distribution influences the out-of-sample volatility forecasting performance using GARCH-N and GARCH-SGED models. Illustrations of these techniques are presented for two main stock markets in China, the daily spot prices of Shanghai and Shenzhen composite stock indices, which are considered more interesting and attractive than that of general developed capital markets. Empirical results indicate that the GARCH-SGED model is superior to the GARCH-N model in forecasting China stock markets’ volatility, for alternative forecast horizons when model selection is based on MSE or MAE. Meanwhile, the DM-tests further confirm that volatility forecasts by the GARCH-SGED model are more accurate than those generated using the GARCH-N model in all cases, indicating the significance of both skewness and tail-thickness in the conditional distribution of returns, especially for the emerging financial markets. 
In the second part, an analytical quantile-operator of the standard HT distribution (Politis, 2004) is derived which facilitates convenient in out-of-sample VaR estimation with HT distribution. In empirical application, we employ GARCH-N, GARCH-t and GARCH-HT models to estimate the one-day-ahead absolute VaR and compare their performance in risk management of competing models. Daily spot prices of WTI crude oil, Brent crude oil, heating oil #2, propane and Conventional Gasoline Regular are used as empirical data to compare the accuracy and efficiency of these VaR models. Empirical results suggest that for asset returns that exhibit leptokurtic and fat-tailed features, the VaR estimates generated by the GARCH-HT models have good accuracy at both low and high confidence levels. Moreover, MRSB measures indicate that the GARCH-HT model is more efficient than alternatives for most cases at high confidence levels. These findings suggest that the heavy-tailed distribution is more suitable for energy commodities, particularly VaR calculation. 
The last part of my dissertation is to contribute to the literature by assessing market risk in the international crude oil market from the perspective of VaR analysis. A GARCH-SGT approach is thus proposed capable of coping with fat-tails, leptokurtosis and skewness using SGT returns innovations and catering for volatility clustering with the GARCH(1,1) model in modeling one-day-ahead VaR. This technique is illustrated using daily returns of West Texas Intermediate crude oil spot prices from December 2003 to December 2007. Empirical results indicate that the VaR forecast obtained by the GARCH-SGT model is superior to that of the GARCH-T and GARCH-GED models through a series of rigorous model selection criteria. Overall, the sophisticated SGT distributional assumption significantly benefits VaR forecasting for WTI crude oil returns at low and high confidence levels, indicating a need for VaR models that consider fat-tails, leptokurtosis and skewness behaviors. This makes the GARCH-SGT model be a robust forecasting approach which is practical to implement and regulate for VaR measurement.

TABLE OF CONTENTS                                                                                              
                                                                    Page
ACKNOWLEDGEMENT                                              i
ABSTRACT IN CHINESE                                             ii
ABSTRACT IN ENGLISH                                             iv
LIST OF TABLES                                                    ix
LIST OF FIGURES                                                   x

PART I	1
Predicting the Volatility of Stock Indices in China Using GARCH Models with Skewed-GED Distribution

ABSTRACT	2
CHAPTER
1. Introduction	3
1.1 Motivations and Objectives	3
1.2 Flow Chart	5
2. Literature Review	6
3. Econometric Methodology	11
3.1 GARCH(1,1) Model with Normal and Skewed-GED Distributions	11
3.2 Volatility Forecasts	13
3.3 Evaluation of Volatility Forecasting Performance	14
3.3.1 Loss Functions	14
3.3.2 Model Significance Test (DM-Test)	15
4. Data Description and Empirical Results	17
4.1 Data Description	17
4.2 Estimation Results	20
4.3 Volatility Forecasting Performance	22
5. Concluding Remarks	25
BIBLIOGRAPHY	27
PART II	30
Modelling Risk for Energy Commodities via Fat-Tailed GARCH Models 

ABSTRACT	31
CHAPTER
1. Introduction	32
1.1 Motivations and Objectives	32
1.2 Flow Chart	34
2. Literature Review	35
3. Econometric Methodology	40
3.1 The GARCH Models with Alternate Conditional Distributions	40
3.1.1 GARCH(1,1) Model with Normal Distribution (GARCH-N)	40
3.1.2 GARCH(1,1) Model with Student t Distribution (GARCH-t)	41
3.1.3 GARCH(1,1) Model with Heavy-Tailed Distribution (GARCH-HT)	42
3.2 Evaluation Methods of Model-Based VaR	44
3.2.1 Binary Loss Function (BLF)	44
3.2.2 Quadratic Loss Function (QLF)	45
3.2.3 LR Test for Unconditional Coverage (LRuc)	45
3.3 Mean Relative Scaled Bias (MRSB)	46
4. Data Description and Preliminary Analysis	48
4.1 Data Description	48
4.2 Preliminary Analysis	48
5. Empirical Results and Analyses	53
5.1 Estimates for the GARCH-N, GARCH-t and GARCH-HT models	53
5.2 Accuracy and Efficiency Measurements	56
5.2.1 VaR Performance for Low Confidence Levels	56
5.2.2 VaR Performance for High Confidence Levels	59
6. Conclusions and Implications	62
APPENDIX	64
BIBLIOGRAPHY	65

PART III	68
Daily Volatility Forecasts with Application to Risk Management: The Role of SGT Distribution in VaR Estimation 

ABSTRACT	69
CHAPTER
1. Introduction	70
1.1 Motivations and Objectives	70
1.2 Flow Chart	73
2. Literature Review	74
3. Econometric Methodology	78
3.1 Conditional Volatility Model	78
3.2 Alternative Distributions	79
3.3 Calculating Value-at-Risk	80
3.4 Evaluating VaR Performance of Competing Models	81
3.4.1 Unconditional Coverage Test (LRuc)	81
3.4.2 Conditional Coverage Test (LRcc)	81
3.4.3 Risk Management Loss Functions	82
3.4.3.1 Regulatory Loss Function (RLF)	83
3.4.3.2 Firm Loss Function (FLF)	83
3.4.3.3 Superiority Tests in Terms of Utility-Based Loss Functions	84
4. Data and Empirical Results	85
4.1 Data Description	85
4.2 Estimation Results and Diagnostic Tests	88
4.3 Analysis of VaR Performance	90
4.3.1 Unconditional and Conditional Coverage Tests Results	90
4.3.2 Model Selection Based on Utility-Based Loss Functions	92
5. Conclusions	95
BIBLIOGRAPHY	97


 
LIST OF TABLES
Page
PART I

Table I.1. Descriptive Statistics of Stock Indices in China	19
Table I.2. Unit Root Tests of Stock Indices in China	20
Table I.3. Estimation Results of Alternate GARCH Models	21
Table I.4. Out-of-Sample Mean Squared Error Statistic	22
Table I.5. Out-of-Sample Mean Absolute Error Statistic	23
Table I.6. DM-Test Results	24

PART II

Table II.1. Descriptive Statistics of Daily Returns	49
Table II.2. Estimation Results of Alternate GARCH(1,1) Models	55
Table II.3. Forecasting Performance Summary for Different VaR Models at Low 
Confidence Levels	58
Table II.4. Forecasting Performance Summary for Different VaR Models at High 
Confidence Levels	60

PART III

Table III.1. Summary Statistics of Crude Oil Returns	86
Table III.2. Estimation Results for Alternatively Competing VaR Models	89
Table III.3. Forecasting Performance Summary of Value-at-Risk Statistics	91
Table III.4. Superiority Tests in Terms of Utility-Based Loss Functions at the 
95% Confidence Level	94




LIST OF FIGURES
Page
PART I

Figure I.1. Descriptive Graphs of Stock Indices in China	18
Figure I.2. Skewed-GED Density Against the Normal Distribution	22

PART II

Figure II.1. Energy Commodities in Levels for Whole Sample	50
Figure II.2. Density of the Daily Returns v.s. Normal Distribution for Whole Sample	51
Figure II.3. The Rolling Window Scheme of the One-Day-Ahead Out-of-Sample 
VaR Forecasts	53

PART III

Figure III.1. Descriptive Graphs of WTI Crude Oil	87
Figure III.2. Daily Returns and Alternative Model-Based VaR Forecasts	92

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